PreprintCC BY 4.0arXiv
Locally analytic representations in mixed characteristic via stacks
Abstract
For any p-adic Lie group G, we construct a group stack Gla over the p-adic branch of Clausen--Scholze's stack of norms such that quasicoherent sheaves on its classifying stack */Gla recover locally analytic representations of G after base change to any suitable Tate Huber pair, even in positive or mixed characteristic. We also show that smooth 𝔽p-representations of G embed fully faithfully into sheaves on the mod p fibre of */Gla and establish Poincaré duality for cohomology of locally analytic representations in mixed characteristic.
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BibTeX
@misc{hauck2026locally,
title = {{Locally analytic representations in mixed characteristic via stacks}},
author = {Maximilian Hauck},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28141},
eprint = {2609.28141},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28141},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Locally analytic representations in mixed characteristic via stacks
AU - Maximilian Hauck
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.28141
UR - https://arxiv.org/abs/2609.28141
AB - For any p-adic Lie group G, we construct a group stack G^la over the p-adic branch of Clausen--Scholze's stack of norms such that quasicoherent sheaves on its classifying stack */G^la recover locally analytic representations of G after base change to any suitable Tate Huber pair, even in positive or mixed characteristic. We also show that smooth 𝔽_p-representations of G embed fully faithfully into sheaves on the mod p fibre of */G^la and establish Poincaré duality for cohomology of locally analytic representations in mixed characteristic.
ER -